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A lot of times you could have seen that you apply force and the shape or size gets changed like archery bow when flexed comes to its original position after arrows are propelled from it, a rubber ball squeezes and a spring gets stretched when you apply force on it. These deformations are what we call strain!
Strain Illustration
Bow stretched by an arrow shows the strain

What is Strain?

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Strain is that deformation seen due to the effect of stress. The deformation may be change in length, volume or any other quantity and is denoted by $\epsilon$. This extension is caused when a body is subjected to a force or set of forces. In general we can can say:

Strain $\epsilon$ = $\frac{Change\ in\ Configuration }{Original\ Configuration}$Since in strain the ratio quantities are same it is unit less and dimensionless.

Strain Formula

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Hooke's law tells about the relationship between stress and strain. According to Hooke's law within the elastic limit stress produced in a body is directly proportional to the strain experienced by it.
Stress Strain Curve
Stress $\propto$ Strain

$\frac{Stress}{Strain}$ = a constant known as Modulus of Elasticity. Its unit is Nm-2.

Types of Strain

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When deforming force is applied on the body it changes the dimension of the body. This is what we call as strain. It is the ratio of change in configuration to the original configuration of the body. It is of three types:

Longitudinal strain: It is the measure of change in length when force acts on it. If l is the original length and the extension is l + $\Delta$ l then it is defined as the ratio of change in length ($\Delta$ l) to the original length l.

Longitudinal Strain $\epsilon$ = $\frac{\Delta l}{l}$

Volumetric strain: When deforming force acts on the body there will be change in the volume of the body. It is ratio of change in volume ($\Delta$ v) to the original volume (v) of the body.

Volumetric Strain $\epsilon$ = $\frac{\Delta v}{v}$

Shear strain: It is the angle through which a face is turned perpendicular to the fixed plane. It is defined as the ratio of displacement of one plane of the body ($\Delta$ D) to its distance from the fixed plane (D).

Shearing strain $\epsilon$ = $\frac{\Delta D}{D}$